{"id":"openai-math/Lechs-multiplicity-conjecture","pdf":"https://github.com/openai/math/blob/main/preprints/Lechs-multiplicity-conjecture-September-23-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/Lechs-multiplicity-conjecture-September-23-2026","tags":["commutative-algebra","multiplicity-theory","algebraic-geometry"],"score":0,"title":"Lech's multiplicity conjecture","domain":"Algebra","family":"194","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.RA","summary":"We prove Lech's multiplicity conjecture: Hilbert–Samuel multiplicity cannot decrease under a flat local homomorphism of nonzero Noetherian local rings. The result holds in arbitrary dimension, with no restrictions on the residue fields or characteristics.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-23","reactions":{},"formalized":false,"family_title":"Lech’s multiplicity conjecture"}